Symmetry-adapted no-core Shell model for light nuclei - [sup 12]C and [sup 16]O

The fundamental role of symmetry in nuclear models

“…The first few irreps in order of increasing E N 1 ,N 2 ,N 3 are shown for 12 C, 16 O and 168 Er in Table 1. The first remarkable result is that for the light nucleus 12 C the lowest three Sp(3, R) irreps are consistent with the states observed in this nucleus as described in an Sp(3, R) model framework by Dreyfuss et al [28,29] whose results are shown in Fig. 10.…”

“…For 16 O, the first-excited state belongs to an irrep whose lowest-weight state would again be 4hω above its unperturbed spherical harmonic oscillator and would lie outside of any normal shell-model valence space. Table 1 by Dreyfuss et al [29]. (The figure is from their preprint with permission.)…”

The structure of the Hoyle state via a measurement of the 'Hoyle Rotational Band' in12C

“…It is shown by the ab-initio NCSpM calculations that the Hoyle state can only be described by up to 20hω shell model space [7], suggesting that it is an extended alpha-clustering configuration.…”

“…A number of models have been proposed to describe the structure of 12 C including a group theoretical U(7) model with a D sh symmetry [3], a microscopic Fermionic Molecular Dynamic (FMD) model [4] together with 'BEC-like' cluster model [5], ab-initio No Core Shell Model (NCSM) [6], ab-initio No Core Simplectic Model (NCSpM) [7], and ab-initio Lattice Effective Field Theory (L-EFT) [8,9]. It is shown by the ab-initio NCSpM calculations that the Hoyle state can only be described by up to 20hω shell model space [7], suggesting that it is an extended alpha-clustering configuration.…”

“…In the frame of the L-EFT theory [9] the Hoyle state is primarily of the bent-arm chain (or obtuse triangular) shape. Both ab-initio NCSpM calculations [7] and L-EFT calculations [9] predict the Hoyle state to be of deformed prolate shape. In addition while the FMD model predicts an rms radius of the Hoyle state (3.48 fm) that is √ 2 larger than the ground state (2.39 fm) [4], calculations in the frame of the ab-initio L-EFT theory [9] predicts an rms radius (2.4 fm) equal (within the predicted error bar) to the rms radius of the ground state of 12 C and the ab-initio NCSpM calculations [7] predict an rms radius (2.93 fm) that is only 22% larger than the ground state of 12 C. The three alpha-particle structure of 12 C naturally leads to models that utilize triangular geometry [3,4,8,9].…”